ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A cotensor in Set is a power

Example

In $S e t$ , the cotensor of a set $C$ by a set $X$ is the power $C^{X}$ .

Facts & Assumptions

Given: Sets $X$ and $C$ .

[L1]

In the special case $V = S e t$ , cotensors are powers (Tensor and cotensor in a V-category).

[L2]

The power $C^{X}$ is characterized by the bijection $S e t (B, C^{X}) ≅ S e t (X, S e t (B, C))$ (The power and the copower of an object by a set).

Verification

technique · direct

1.1

The universal property in [L2] is exactly the $S e t$ -instance of the cotensor formula from [L1].

L1L2given

2.1

Therefore the cotensor of $C$ by $X$ in $S e t$ is the power $C^{X}$ .

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

11 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Emily Riehl, Categorical Homotopy Theory, Section 3.7 (standard reference, not scraped)